The problem of finding the shortest path in a graph is widely applicable in the real world. Many things are mathematically modeled using graphs, which creates the need for better and faster algorithms to solve this problem. Examples are various types of roads and traffic situations, Internet networks, special types of databases, and various others. The first part of this thesis is dedicated to classical algorithms that do not require preprocessing. The Dijkstra’s algorithm and the A\( ^*\) algorithm, and their two-way versions are described. More recently, the key to accelerating finding the shortest path in algorithms lies in the preprocessing phase. By performing the necessary procedures, the algorithm collects the information it uses to speed up the path search phase. We describe two such algorithms in detail: Contraction Hierarchies and Landmark A\( ^*\). The Contraction Hierarchies algorithm appropriately determines the hierarchy of vertices and adds new edges called shortcuts to the initial graph. The shortest path finding is performed by a two-way Dijkstra’s search in a modified graph where both searches search only the edges leading to the tops of the larger hierarchy. The Landmark A\( ^*\) algorithm is based on A\( ^*\) search with a heuristic distance estimation function obtained by the preprocessing phase. We introduce the landmark nodes for which the distance from and to all remaining nodes is known. The estimate of the distance is obtained based on the triangle inequality. In the last part, we compare the observed algorithms and present some implementation details. The results were obtained on the basis of actual road network data. Contraction Hierarchies outperforms the Landmark A\( ^*\) algorithm in the speed of finding the shortest path, but with a longer preprocessing time. Depending on the time allowed and the available memory during the preparation phase, a more suitable algorithm is chosen. Both algorithms are significantly faster compared to the classic Dijkstra’s search.